In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal'cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case. Another counterexample, of a different nature, was independently given recently by Steinberg. Taking these two counterexamples into account, we propose a modified version of our conjecture and some supporting evidence for that new formulation. We show in particular that a solution to our new conjecture would give a solution of the decidability of the levels 2 of the Straubing–Thérien hierarchy and of the dot-depth hierarchy. Consequences for the other levels are also discussed.

We prove that a word of length n from a finitely ambiguous context-free language can be generated at random under uniform distribution in O(n 2 log n) time by a probabilistic random access machine assuming a logarithmic cost criterion.We also show that the same problem can be solved in polynomial time for every language accepted by a polynomial time 1-NAuxPDAwith polynomially bounded ambiguity.

We say that two languages X and Y are conjugates if they satisfythe conjugacy equationXZ = ZY for some language Z. We studyseveral problems associated with this equation. For example, wecharacterize all sets which are conjugated via a two-element biprefixset Z, as well as all two-element sets which are conjugates.

In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties.The new mapping is based on square matrices of a certain form. The classical Parikh vectorappears in such a matrix as the second diagonal.However, the matrix product gives more information abouta word than the Parikh vector. We characterize the matrixproducts and establish also an interesting interconnectionbetween mirror images of words and inverses of .

We give a partial answer to a question of Carlitz asking for aclosed formula for the number of distinct representations of aninteger in the Fibonacci base.

This paper surveys the area of Free Burnside Semigroups. The theory of these semigroups, as is the case for groups, is far from being completely known. For semigroups, the most impressive results were obtained in the last 10 years. In this paper we give priority to the mathematical treatment of the problem and do not stress too much neither motivation nor the historical aspects. No proofs are presented in this paper, but we tried to give as many examples as was possible.

We introduce the notion of a k-synchronized sequence, where k is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be k-synchronized if its graph is represented, in base k, by a right synchronized rational relation. This is an intermediate notion between k-automatic and k-regular sequences. Indeed, we show that the class of k-automatic sequences is equal to the class of bounded k-synchronized sequences and that the class of k-synchronized sequences is strictly contained in that of k-regular sequences.Moreover, we show that equality of factors in a k-synchronized sequence is represented, in base k, by a right synchronized rational relation. This result allows us to prove that the separator sequence of a k-synchronized sequence is a k-synchronized sequence, too. This generalizes a previous result of Garel, concerning k-regularity of the separator sequences of sequences generated by iterating a uniform circular morphism.

In this paper methods and results related to the notion of minimalforbidden words are applied to the fragment assembly problem. Thefragment assembly problem can be formulated, in its simplest form,as follows: reconstruct a word w from a given set I ofsubstrings (fragments) of a word w. We introduce anhypothesis involving the set of fragments I and the maximallength m(w) of the minimal forbidden factors of w. Suchhypothesis allows us to reconstruct uniquely the word w from theset I in linear time. We prove also that, if w is a wordrandomly generated by a memoryless source with identical symbolprobabilities, m(w) is logarithmic with respect to the size ofw. This result shows that our reconstruction algorithm is suitedto approach the above problem in several practical applicationse.g. in the case of DNA sequences.

A wheeled mobile manipulator system is modeled using Kane's dynamic equations. Kane's equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane's approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints associated with slipping and skidding as well as conditions for avoiding tipping over are included. The resulting equations, along with the set of constraint equations provide a safe and complete framework for developing control strategies for mobile manipulator systems.

This paper presents a new calibration method for industrial robots. The calibration method is based on a combination of inclinometer and LVDT measurements and is very simple to use. The inclinometers measure the deviation from the gravity direction of a measurement rod and the LVDT sensor measures the length of the rod. The inclinometers can be used without any pre-calibration and the whole equipment is inexpensive, portable and robust.

A neuroadaptive control scheme for elastic-joint robots is proposed that uses a relatively small neural network. Stability is achieved through standard Lyapunov techniques. For added performance, robust modifications are made to both the control law and the weight update law to compensate for only approximate learning of the dynamics. The estimate of the modeling error used in the robust terms is taken directly from the error of the network in modeling the dynamics at the currant state. The neural network used is the CMAC-RBF Associative Memory (CRAM), which is a modification of Albus's CMAC network and can be used for robots with elastic degrees of freedom. This results in a scheme that is computationally practical and results in good performance.

Traditional expert systems for fault diagnosis have a bottleneck in knowledge acquisition, and have limitations in knowledge representation and reasoning. A new expert system shell for fault diagnosis is presented in this paper to develop multiple knowledge models (object model, rules, neural network, case-base and diagnose models) hierarchically based on multiple knowledge. The structure of the expert system shell and the knowledgerepresentation of multiple models are described. Diagnostic algorithms are presented for automatic modeling and hierarchical reasoning. It will be shown that the expert system shell is very effective in building diagnostic expert systems.

In this paper fhe problem of motion control of a biped is considered. We develop a new method based on multi-agent associated Neural AIGLS (On-line Augmented Integration of Gradient and Last Sguare method) – RSPN (Recursive Stochastic Petri Nets) strategy. This method deals with organization and coordination aspects in an intelligent modeling of human motion. We propose a cooperative multi-agent model. Based on this model, we develop a control kernel named IMCOK (Intelligent Motion COntrol Kernel) which consists of a controller, a coordinator and an executor of different cycles of the motion of the biped. When walking, IMCOK receives messages and sends offers. A Decision Making of Actions (DMA) is developed at the supervisor level. The articulator agents partially planify the motion of the associated non-articulator agents. The system is hybrid and distributed functionally. The learning of the biped is performed using an On-line Augmented Integration of Gradient and Last Sguare Neural Networks based algorithm. In the conflictual situations of sending or receiving messages by the managers of MABS we apply a new strategy: Recursive Stochastic Petri Nets (RSPN). This module is fundamental in the On-line information processing between agents. It allows particularly the Recursive strategy concept. Cognitive agents communicate with reactive (non-articulator) agents in order to generate the motion.

In this paper we propose a set of techniques for a real-time motion capture of a human body. The proposed motion capture system is based on low cost accelerometers, and is capable of identifying the body configuration by extracting gravity-related terms from the sensor data. One sensor unit is composed of 3 accelerometers arranged orthogonally to each other, and is capable of identifying 2 rotating angles of joints with 2 degrees of freedom. A geometric fusion technique is applied to cope with the uncertainty of sensor data. A practical calibration technique is also proposed to handle errors in aligning the sensing axis to the coordination axis. In the case where motion acceleration is not negligible compared with gravity acceleration, a compensation technique to extract gravity acceleration from the sensor data is proposed. Experimental results not only for individual techniques but also for human motion capturing with graphics are included.

In this paper a new concept, named the Extended Operational Space (EXOS), has been proposed for the effective analysis and the real-time control of the robot manipulators with kinematic redundancy. The EXOS consists of the operational space (OS) and the optimal null space (NS): the operational space is used to describe manipulator end-effector motion; whereas the optimal null space, described by the minimum number of NS vectors, is used to express the self motion.

Based upon the EXOS formulation, the kinematics, statics, and dynamics of redundant manipulators have been analyzed, and control laws based on the dynamics have been proposed. The inclusion of only the minimum number of NS vectors has changed the resulting dynamic equations into a very compact form, yet comprehensive enough to describe: not only the dynamic behavior or the end effector, but also that of the self motion; and at the same time the interaction of these two motions. The comprehensiveness is highlighted by the demonstration of the dynamic couplings between OS dynamics and NS dynamics, which are quite elusive in other approaches.

Using the proposed dynamic controls, one can optimize a performance measure while tracking a desired end-effector trajectory with a better computational efficiency than the conventional methods. The effectiveness of the proposed method has been demonstrated by simulations and experiments.

The design of prosthetic hands is constrained by a series of strict conditions. Despite this, many different design strategies have been explored. One particular form is the Southampton Hand system. This is a hierarchically controlled, electrically driven hand, with multiple axes, in an anthropomorphic form. This paper details the range of mechanical solutions adopted to address the conditions. It also compares them with other solutions.

In this work another perturbation estimation sliding mode based control algorithm is introduced for a class of robotic systems in the presence of structured and unstructured uncertainties and external disturbances. The effects of these uncertainties are combined into a single quantity. A full order device with the actuator voltages as control inputs is assumed in control design. The decentralized control scheme with only a partial state feedback is applied. A modification of the switching functions with perturbation estimation is introduced. The salient features of this approach is that the perturbations are effectively treated by a computationally straightforward procedure. The proposed controller is applied to a minimal configuration direct drive robot mechanism.

When a parallel manipulator reaches a singular configuration (singularity), the end effect (platform) pose cannot be controlled any longer, and infinite active forces must be applied in the actuated joints to balance the loads exerted on the platform. Therefore, these singularities must be avoided during motion. The first step to avoid them is to locate all the platform poses (singularity locus) making the manipulator singular. Hence, the availability of a singularity locus equation, explicitly relating the manipulator geometric parameters to the singular platform poses, greatly facilitates the design process of the manipulator. The problem of determining the platform poses, that make the 6-3 fully-parallel manipulator (6-3 FPM) singular, will be addressed. A simple singularity condition will be written. This singularity condition consists in equating to zero the mixed product of three vectors, that are easy to be identified on the manipulator, and it is geometrically interpretable. The presented singularity condition will be transformed into an equation (singularity locus equation) explicitly containing the geometric parameters of the manipulator and the platform pose parameters making the 6-3 FPM singular. Eventually, the singularity locus equation will be reduced to a polynomial equation by using the Rodrigues parameters to parameterize the platform orientation. This polynomial equation is cubic in the platform position parameters and one of sixth degree in the Rodrigues parameters.

Robot manipulators, which are nonlinear structures and have uncertain system parameters, are complex dynamically when operated in an unknown environment. To compensate for estimate errors of the uncertain system parameters and to accomplish the desired trajectory tracking, nonlinear robust controllers are appropriate. However, when estimation errors or tracking errors are large, they require large input torques, which may not be satisfied due to torque limits of actuators such as driving motors. As a result, their stability cannot be guaranteed. In this paper, a new robust control scheme is presented to solve stability problems and to achieve fast trajectory tracking of uncertain robot manipulators in the presence of torque limits. By using fuzzy logic, new desired trajectories which can be reduced are generated based on the initial desired trajectory, and torques of the robust controller are regulated so as to not exceed torque limits. Numerical examples are shown to validate the proposed controller using an uncertain two degree-of-freedom underwater robot manipulator.